In this study, rigour is concerned more specifically with the validity and reliability of the research process, that is, the appropriateness, meaningfulness and usefulness of the claims that I, a researcher, make (Sanni, 2009). Given this need for integrity, I worked rigorously
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with the data collection and data analysis as well as with the existing theory and literature in order to make careful links between them and evolve a qualitative work worthy of the trust and confidence of the readers.
In the context of my study, “validity is described as the degree to which a method, a test or a research tool actually measures what it is supposed to measure” (Merriam, 2009, p. 354). Reliability, on the other hand, is an important consideration in that it may be useful as an indicator of trustworthiness or quality of the research. Thus, Creswell (2007) further describes reliability as “the extent to which a test, method or instrument gives unswerving results across a range of settings used by a range of researchers” (p. 274). Reliability simply means dependability, stability, consistency and accuracy (Lincoln and Guba, 2003). It is the “extent to which a measuring instrument yields a similar result on repeated applications with different subjects in different contexts” (Atebe, 2008, p. 125).
3.6.1. Ensuring validity of my study
As Schäfer (2003, p. 69) notes “validity is not seen as part of a final product control process or verification, but rather a continuous process of credibility, growth and understanding”. From this perspective, data validation is a complex and rather multifaceted, and thus requires careful consideration. Viewed as the key issue and requirement for both qualitative and quantitative research methods, validation of data in this study was deemed more necessary in the context of my work to “accurately describe the phenomena being researched” (Cohen et al., 2007, p. 113). Validity issues that I needed to be aware of, or deal with, are discussed below.
3.6.1.1. Researcher bias
I needed to be conscious of and make explicit any assumptions, values, beliefs and theories that I bring to the research process in order to avoid leading the interviewees through my questions and actions. It is important that I acted with integrity at all times (Maxwell, 2008).
3.6.1.2. Rich data
Rich data were collected through the geometry questionnaire, non-participant classroom lesson observations of teaching and intensive interviews with the research participants. Also, as a researcher, I excluded any of my own experiences within the community of practice and focused on the teachers’ viewpoints.
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3.6.1.3. A team of expert researchers and critical friends
The help of critical friends was beneficial in shaping up my “research ideas and enhancing reflection on the research process” (Muir, 2010, p. 43). As part of a PhD research discussion group where we share our research ideas and work, a team of peers (PhD fellows) and expert researchers (research-minded people) have been involved in the research and the data validation process in one way or another. This is a space where colleagues can question the research process, the data and emerging findings. Such a team of critical friends was fundamental and explicitly facilitated the validation process of the research findings.
Most importantly, my supervisor for this study played an integral role in the validation of the research process, by scrutinising my arguments with regard to the data analysis and presentation, classroom observation schedule/tool and interview questions. All the way through the process, he offered different critical perspectives to issues but also enriched both the research process and my engagement with the project. As Schäfer (2003) concedes, “validation does not imply that the goal is to achieve uniformity in the criticism, but rather that the views are valid, meaningful and useful” (p. 72). Throughout the research process, the findings, suggestions and alternative explanations that emerged from the supportive team of critical friends were taken into account and acted upon as a means of establishing clarity in the research.
3.6.1.4. Progressive subjectivity
As another validation technique, my subjectivity, interpretation and ideas cannot be “given privilege over that of anyone else” (Schäfer, 2003, p. 72). For Schäfer, the matter is not whether the constructs are subjective or not, but rather whether they have been sufficiently opened to the light of criticism.
3.6.1.5. Collegial team of co-researchers (member checking)
This validation modus operandi sometimes referred to as participant validation, involved a team of five participating teachers as co-researchers and several expert researchers to tease out and verify my analysis and interpretation of themes. As Schäfer (2003) notes, member checking is “[a] crucial technique for establishing credibility” (p. 73). Member checking was achieved via feedback from the participants once the interviews had been transcribed to ensure that the data accurately reflected the participants’ experiences. This technique was applied particularly during phase VI; stage III, of this research project. Further, at the level of
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analysis, findings were shared with several critical colleagues. Such a collegial team of co- researchers comprised:
five participating teachers as co-researchers who were involved in the research as effective teachers, and who were given copies of the interview transcripts to help secure the interpretive validity of the research.
a mathematics educator and a post-doctoral research fellow in teacher professional development. His research work focused on mathematics argumentation and was firmly embedded in an interpretive research paradigm. His data analysis was on the interpretation of lesson video recordings of teachers in action.
3.6.1.6. Triangulation
I used multiple sources of data. In this research teachers’ biographical and geometry questionnaires, classroom observations and interviews were used as data for analysis. In addition, in an attempt to ensure validity, my proposed data collection tools draw from recently established models on teaching proficiency or robust mathematics instructions and developed classroom observation instruments relevant to the practice of teaching. After constructing a geometry questionnaire, experts in geometry were requested to cross-check them. The test items were selected and adapted from standardized examinations that have passed through various validity-testing processes. A comprehensive lesson observation tool or checklist was developed based on Kilpatrick et al.’s (2001) model and the enactivist framework. This was crafted and then face-validated with the assistance of specialists at the Rhodes University Department of Education. In addition, I implemented a procedure proposed by Atebe (2008). In this framework, a consultative panel of independent observers was involved to view the videotaped lessons and make comments on the manner in which information was captured and the quality of data interpretation. In this process, I concentrated on achieving conformability, credibility and transferability (Cohen et al., 2007).
3.6.2. Ensuring reliability of my study
What follows are some of the measures that I took to ensure the reliability of my research instruments. In terms of the geometry content knowledge questionnaire, I sourced items that have been used before and did some modification, where necessary, to suit my study needs, before conducting a reliability test (piloting) for the individual items. Further, I piloted both the lesson observation schedule and interview questions. This was achieved by viewing an existing recorded mathematics lesson video with Rhodes University Masters of Education
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students. With regard to the analysis strategies and interpretation of audio transcripts of both lessons and interviews with teachers, I involved all five participating teachers plus other researchers in the analysis and checking of collected qualitative data. I therefore verified my interpretations of what I observed in their lessons, (a) the emerging patterns of their individual lessons and (b) interactions across the five teachers’ lessons or classrooms.